There are different stake holders like the quality team,client, peers, sub-ordinates, seniors. As a manager, do we need to have a strategy to handle different stakeholders? Sometimes we might not be able to be good to everyone. In such a scenario, whom we need to give priority and based on what?
It is not subjective at all. It is the result of your stakeholder analysis, a necessary analysis that feeds your communication plans, your training plans, your stakeholder participation plans, and likely many other things. It is one of the most important things you do for your project and this is not an area where you want to go on the cheap or try to save money or even try to avoid doing. It is a must.
You need to segment your stakeholders into categories of similar attributes. Then you need to ask the questions like who are they, what do they need, what do we need from them, how will they be impacted, are they likely supporters or detractors of this project, what do they need to hear, what do we need to hear from them.
You are right that not all stakeholder segments will benefit from the project. That is very unlikely. One or more stakeholders are going to get impacted in an unfavorable way and part of your plan needs to include how to manage that, including bulldozing them out of the way (as atrocious as that might sound).
Bottom line is, your stakeholder management activities need to be as complex and diverse as your stakeholder community is. Anything less you are increasing the odds of failure.
As part of your project start-up documentation, you can (and should) describe what you will deliver to satisfy each of your stakeholders. I would normally include this in the Project Initiation Document (PID), which must be signed off by the principal stakeholders.
For each stakeholder, you should define the relationship, and what you will deliver to meet their requirements. It will be a short description for some, and a much more extensive write-up for others. In each case, you should be identifying what you will do, and what you won't -and this should include your communication strategy for that stakeholder, as well as "hard" deliverables.
In terms of priorities, that will vary according to the project. For example, in a defence or medical project, you may have quality as a very high priority, whereas in banking the focus may be more on regulatory matters. In some cases, the customer experience may be highly significant, and in others, cost control may be at the top of the agenda. Discuss this with your project sponsor and gain his or her agreement. That way, you both know what is expected.
The project sponsor is generally the most important stakeholder to your project. Without the sponsor, the project wouldn't exist (from a funding/empowered to use resources perspective) and the project wouldn't have a reason to exist (the project exists to provide a result for the sponsor -your customer).
If you have trouble working with a particular stakeholder group, identify why that problem exists and address it.
First of all, go talk with them. How do they wish to be informed about the project? Do they want your regular status report? Do they wish to be informed about scope progress? The lot or only that one feature one of them has requested? Ask, then decide (and document) how to keep each of them in the loop.
Regarding priority, that depends upon their "stake" in the project. But it should be discussed and agreed by your SteerCo how you will handle priority issues.
For you to prioritize stakeholders you would need to connect them to enabling your project's goals/sub-goals.
Prioritize your project goals and you should have a prioritized list of stake holders
There are three important things to consider:
What is the formal process? As mentioned by @lain9688 you should have some sort of Project Initiation or kickoff document. This should include who each party is, and for each activity or deliverable, what their level of involvement is. (Own? Contribute? Veto?) What is the real capability? Many times Statements of Work or Initiation Documents are written that don't fully capture reality. As a good project Manager you need to be on top of where the breakdown is. Will your client really ever pay for Change Requests? Will an external Design Authority really be fast enough? Will there really be enough time for the project team to analyze all the new requirements? Lastly, what is the relative importance of the stakeholders. Usually the most important is the one that's paying, but sometimes others have veto power, or aren't cooperative. Many times someone will say, "I'm paying for this, my team will honor all the industry standards" but then their subordinates want a million free customizations. This is a big challenge in project management.